Alain Pumir
École Normale Supérieure, Physique, Faculty Member
Research Interests: Physics, Turbulence, Medicine, Chaos Theory Evolution Equation, Anisotropy, and 13 moreSpatial Scale, Physical, Second Order, Turbulent Mixing, Three Dimensional, Large Scale, Probability Density Function, Velocity Field, Direct Numerical Simulation (DNS), X, Isotropy, Evolution Equation, and perpendicular
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A pointwise, infinite stretching is found in a simulation of the Biot-Savart equation for a vortex tube in three dimensions. The relevance of this result to the incompressible Euler and Navier-Stokes equations is discussed. Permanent... more
A pointwise, infinite stretching is found in a simulation of the Biot-Savart equation for a vortex tube in three dimensions. The relevance of this result to the incompressible Euler and Navier-Stokes equations is discussed. Permanent address: D-PhG/SPT, CEN Saclay, L'Ormedes-Merisiers F-91191, Gif-sur-Yvette, France.
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Most studies of collisions in turbulent flows are based on the "ghost collision" approximation, whereby one follows a number of particles, and simply counts the number of times the distance between two particles becomes... more
Most studies of collisions in turbulent flows are based on the "ghost collision" approximation, whereby one follows a number of particles, and simply counts the number of times the distance between two particles becomes less than the sum of their radii; particles are kept in the flow after they collided. We discuss here the limitations of this approximation, and demonstrate,
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ABSTRACT Pattern formation occurs spontaneously in endothelial cell cultures, leading to the formation of capillary networks, which eventually grow to form blood vessels. This phenomenon occurs on a time scale of a few days. We show here... more
ABSTRACT Pattern formation occurs spontaneously in endothelial cell cultures, leading to the formation of capillary networks, which eventually grow to form blood vessels. This phenomenon occurs on a time scale of a few days. We show here that patterns can also be induced on a much shorter time scale, by using the Faraday hydrodynamic instability, resulting from an oscillatory motion of the container. Close to the threshold of instability, the patterns observed are very sharp concentric rings or stripes. The patterns can be induced only inside a very narrow time window, ∼5min. Cells attachment then develops, and pattern formation can no longer be induced. The time window for pattern formation was diminished by favoring cell attachment, for instance by treating culture dishes with cationic macromolecules, such as poly-L-Lysine. It was increased by cooling the cells to 18 ∘ C, or by a prolonged exposure of the cells to trypsin, which is known to digest adhesion molecules.
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We investigate theoretically the possibility to control the transition between two metastable states in reactive systems by imposing a spatial modulation. In particular, we consider the technologically very important case of the... more
We investigate theoretically the possibility to control the transition between two metastable states in reactive systems by imposing a spatial modulation. In particular, we consider the technologically very important case of the transition between the low temperature (nucleate boiling) and the high temperature (film boiling) phases of boiling of a liquid over a heat generating element, also known as the boiling crisis. With the help of a simplified model, we demonstrate that the dangerous regime where the high temperature phase invades the whole system requires a larger heat power in a periodically spatially modulated system, than in a uniform system. The possibility that a local perturbation, such as a small gas bubble, may induce locally a transition to the film boiling state is also considered. We show that the transition to the film boiling regime is hindered in a spatially periodic system. (c) 2002 American Institute of Physics.
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A three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are... more
A three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are quasi-two-dimensional and the vorticity has a pronounced tendency to develop sharp jumps in magnitude. The vorticity is very nearly parallel to the eigenvector of the rate-of-strain matrix whose
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A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of... more
A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.
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In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by... more
In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis, and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as t^{3}. We also find the geometric deformation of material volumes, defined by four points spanning an initially regular tetrahedron, to show sensitivity to the time reversal with an effect growing linearly in t. We associate this with the structure of the strain rate in the flow.
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Research Interests: ice crystals and settling
Research Interests: Physics, Mechanics, Turbulence, Medicine, Anisotropy, and 3 morePhysical sciences, Inertia, and settling
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We investigate the response of energy flux in isotropic turbulence to step-function like perturbation in external forcing at large length scales. From both physical experiments and direct numerical simulations, we measured the evolution... more
We investigate the response of energy flux in isotropic turbulence to step-function like perturbation in external forcing at large length scales. From both physical experiments and direct numerical simulations, we measured the evolution of the Eulerian velocity structure functions, such as $D_{LL}(r)$, $D_{NN}(r)$, before and after the perturbation in forcing. In both cases, we observed the cascade of the energy excess at large scales cascade through scales to the dissipative range, which can be used to study the dynamics of the cascade, and in particular, to estimate the relevant time scales.
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We derive from first principles analytic relations for the second- and third-order moments of $\boldsymbol{\mathsf{m}}$ , the spatial gradient of fluid velocity $\boldsymbol{u}$ , $\boldsymbol{\mathsf{m}} = \nabla \boldsymbol{u}$ , in... more
We derive from first principles analytic relations for the second- and third-order moments of $\boldsymbol{\mathsf{m}}$ , the spatial gradient of fluid velocity $\boldsymbol{u}$ , $\boldsymbol{\mathsf{m}} = \nabla \boldsymbol{u}$ , in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second- and third-order moments of the velocity gradient experimentally for isotropic compressible turbulence.
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Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and... more
Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and pressure-Hessian—which are analysed here using direct numerical simulations of isotropic turbulence on up to 12 288 3 grid points, and Taylor-scale Reynolds numbers in the range 140–1300. We extract the statistics involved in amplification of strain and condition them on the magnitude of strain. We find that strain is self-amplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the mean-field and hence depletes intense strain. Analysing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. By contrast, the self-amplification acts to deplete th...
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<p>Dependence on <i>G</i><sub><i>m</i></sub> of the quantities characterizing the patterns of activity shown in <a... more
<p>Dependence on <i>G</i><sub><i>m</i></sub> of the quantities characterizing the patterns of activity shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0118443#pone.0118443.g008" target="_blank">Fig. 8</a>, namely the mean values of (a) <i>T</i><sub><i>a</i></sub>, (b) <i>T</i><sub><i>r</i></sub>, and (c), <i>T</i><sub><i>f</i></sub> (c); and of the number of (d) action potentials, <i>N</i><sub><i>r</i></sub>, and (e) fast oscillations, <i>N</i><sub><i>f</i></sub>. The error bars indicate the standard deviation of the fluctuations of each individual quantity. Each quantity is measured over an interval of at least 6000 s. The quantities shown here have been determiend after averaging over 30 independent realizations of the passive cell distribution.</p
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Collisions, resulting in aggregation of ice crystals in clouds, is an important step in the formation of snow aggregates. Here, we study the collision process by simulating spheroid-shaped particles settling in turbulent flows and by... more
Collisions, resulting in aggregation of ice crystals in clouds, is an important step in the formation of snow aggregates. Here, we study the collision process by simulating spheroid-shaped particles settling in turbulent flows and by determining the probability of collision. We focus on platelike ice crystals (oblate ellipsoids), subject to gravity, and to the Stokes force and torque generated by the surrounding fluid. We also take into account the contributions to the drag and torque due to fluid inertia, which are essential to understand the tendency of crystals to settle with their largest dimension oriented horizontally. We determine the collision rate between identical crystals, of diameter 300 μm, with aspect ratios in the range 0.005 ≤ β ≤ 0.05, and over a range of energy dissipation per unit mass, ε, 1 ≤ ε ≤ 250 cm2 s−3. For all values of β studied, the collision rate increases with the turbulence intensity. The dependence on β is more subtle. Increasing β at low turbulence ...
Research Interests: Physics, Mechanics, Turbulence, Atmospheric sciences, Drag, and 3 moreCOLLISION, Inertia, and ice crystals
In a channel flow, the velocity fluctuations are inhomogeneous and anisotropic. Yet, the small-scale properties of the flow are expected to behave in an isotropic manner in the very-large-Reynolds-number limit. We consider the statistical... more
In a channel flow, the velocity fluctuations are inhomogeneous and anisotropic. Yet, the small-scale properties of the flow are expected to behave in an isotropic manner in the very-large-Reynolds-number limit. We consider the statistical properties of small-scale velocity fluctuations in a turbulent channel flow at moderately high Reynolds number ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$), using the Johns Hopkins University Turbulence Database. Away from the wall, in the logarithmic layer, the skewness of the normal derivative of the streamwise velocity fluctuation is approximately constant, of order 1, while the Reynolds number based on the Taylor scale is$R_{\unicode[STIX]{x1D706}}\approx 150$. This defines a small-scale anisotropy that is stronger than in turbulent homogeneous shear flows at comparable values of$R_{\unicode[STIX]{x1D706}}$. In contrast, the vorticity–strain correlations that characterize homogeneous isotropic turbulence are nearly unchanged in channel flow even...
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Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion... more
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterise the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the 'butterfly effect' needs to be carefully qualified. We argue that the combination of mi...
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Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of... more
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
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The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not... more
The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled t...
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Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We... more
Three particles floating on a fluid surface define a triangle. The aim of this paper is to characterise the shape of the triangle, defined by two of its angles, as the three vertices are subject to a complex or turbulent motion. We consider a simple class of models for this process, involving a combination of a random strain of the fluid and Brownian motion of the particles. Following D. G. Kendall, we map the space of triangles to a sphere, whose equator corresponds to degenerate triangles with colinear vertices, with equilaterals at the poles. We map our model to a diffusion process on the surface of the sphere and find an exact solution for the shape distribution. Whereas the action of the random strain tends to make the shape of the triangles infinitely elongated, in the presence of a Brownian diffusion of the vertices, the model has an equilibrium distribution of shapes. We determine here exactly this shape distribution in the simple case where the increments of the strain are ...
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Submitted for the DFD15 Meeting of The American Physical Society Dynamics of the tetrad-based velocity gradient in turbulent flows HAITAO XU, Center for Combustion Energy, Tsinghua University, Beijing 100084, China and MPI Dynamics &... more
Submitted for the DFD15 Meeting of The American Physical Society Dynamics of the tetrad-based velocity gradient in turbulent flows HAITAO XU, Center for Combustion Energy, Tsinghua University, Beijing 100084, China and MPI Dynamics & Self-Organization (MPIDS), Goettingen 37077, Germany, ALAIN PUMIR, ENS Lyon, Lyon 69007, France, EBERHARD BODENSCHATZ, MPI Dynamics & Self-Organization (MPIDS), Goettingen 37077, Germany — We investigate the structure and evolution of turbulent flows with the help of the perceived velocity-gradient, determined from four fluid particles initially forming a regular tetrad of size r0. The main feature of the turbulent dynamics can be conveniently captured by a reduced description, in terms of two invariants of the velocity gradient. When r0 is in the inertial range of scales, the evolution of averaged quantities can be parametrized by two dimensionless parameters, which vary slowly with r0. We also characterize the fluctuations around the conditional mean,...